Finite Group Databasebeta

← C3×D15×D155 #42124909

Subgroups — C3×D15×D155 #42124909

Order 27900.

212 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×D155C211yesmaximal, characteristic, complemented
2C3×C5×D15×C31C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊D155)C211yesmaximal, characteristic, complemented
4D15×D155C311yesmaximal, characteristic, direct product factor
5C3×D5×D155—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C3×D3×D155—51nomaximal
8C3×D15×D31—51nomaximal
9C3⋊(C5⋊D155)C2×C311yescharacteristic, complemented
10C5×D15×C31C2×C311yescharacteristic, complemented
11C3×C5⋊D155—31no—
12C3×C5×D155—21no—
13C3×C5×D155D311yescharacteristic, complemented
14C3×C5×D155C2×C311yescharacteristic, complemented
15C3×C5×D5×C31—31no—
16D5×D155—31noHall
17C3×D465—51no—
18C3×D465—51no—
19C3×D465—102no—
20C3×D15×C31D511yescharacteristic, complemented
21C3×C5×D3×C31—51no—
22C32×D155D511yescharacteristic, complemented
23C32×C5×D31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×C3×D155—151no—
28D3×D155—51no—
29D15×D31—51no—
30C3×D5×D31—151no—
31C5⋊D155—31no—
32C5×D155C3×D311yescharacteristic, complemented
33C5×D5×C31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C2×D511yescharacteristic, complemented
37C3×D3×D31—251noHall
38C2×C3×C5×C31—151no—
39D465—51no—
40D465—51no—
41D465—102no—
42D15×C31C3×D511yescharacteristic, complemented
43C5×D3×C31—51no—
44C3×D155—21no—
45C3×D155—151no—
46C3×D155—151no—
47C3×D155—302no—
48C3×D155C3×D511yescharacteristic, complemented
49C3×D155D1511yescharacteristic, direct product factor
50C3×D5×C31—31no—
51C3×C5×D31—51no—
52C3×C5×D31—51no—
53C3×C5×D31—101no—
54C3×D5×D15—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×D155—151no—
57D5×D31—151no—
58C3×D93—251no—
59C3×D3×C31—51no—
60C32×D31—51no—
61C3×C5×C31—21no—
62C3×C5×C31—21no—
63C3×C5×C31—22no—
64C3×C5×C31—22no—
65C3×C5×C31—42no—
66C3×C5×C31D3×D511yescharacteristic, complemented
67C3×C5×C31C2×C3×D511yescharacteristic, complemented
68C3×C5×C31C2×C3×D511yescharacteristic, complemented
69C3×C5×C31C2×D1511yescharacteristic, complemented
70C3×C3⋊(C5⋊D5)—311no—
71C3×C5×D15D3111yescharacteristic, complemented
72C32×C5×D5—311no—
73C2×C3×D31—751no—
74D3×D31—251no—
75C2×C5×C31—151no—
76D155—151no—
77D155—151no—
78D155—302no—
79D155C3×D1511yescharacteristic, direct product factor
80C5×D31—51no—
81D5×C31—31no—
82D5×D15—311no—
83C3×D52—931no—
84C32×C31D5211yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86C2×C3×C31—151no—
87D93—251no—
88C3×D31—51no—
89C3×D31—51no—
90C3×D31—101no—
91C3×D31—751no—
92D3×C31—51no—
93C2×C3×D15—1551no—
94C3×D3×D5—1551no—
95C5×C31—22no—
96C5×C31C3×D3×D511yescharacteristic, complemented
97C5×C31C2×C3×D1511yescharacteristic, complemented
98C3⋊(C5⋊D5)—311no—
99C5×D15C3×D3111yescharacteristic, complemented
100C3×C5⋊D5—931no—
101C3×C5×D5—31no—
102C3×C5×D5—311no—
103C3×C5×D5—311no—
104C3×C5×D5—621no—
105C2×D31—751noHall
106D52—931noHall
107C3×C31—21no—
108C3×C31C3×D5211yescharacteristic, complemented
109C3×C31D5×D1511yescharacteristic, complemented
110C2×C32×C5—1551no—
111C3×D15—3102no—
112C3×D15—1551no—
113C3×D15—1551no—
114C3×D15D15511yescharacteristic, direct product factor
115C3×C5×D3—51no—
116C32×D5—311no—
117C3×C52—21no—
118C3×C52D3×D3111yescharacteristic, complemented
119C3×C52C2×C3×D3111yescharacteristic, complemented
120C2×C31—151no—
121D31—51no—
122D31—751no—
123C2×D15—1551no—
124C2×C3×D5—4651no—
125C2×C3×D5—4651no—
126D3×D5—1551no—
127C5⋊D5—931no—
128C5×D5—31no—
129C5×D5—311no—
130C32×C5—22no—
131C32×C5D5×D3111yescharacteristic, complemented
132C32×C5C2×D15511yescharacteristic, complemented
133C2×C3×D3—7751noHall
134C31C3×D5×D1511yescharacteristic, complemented, Sylow
135C2×C3×C5—151no—
136C2×C3×C5—3101no—
137C2×C3×C5—1551no—
138C2×C3×C5—1551no—
139D15—3102no—
140D15—1551no—
141D15—1551no—
142D15C3×D15511yescharacteristic, direct product factor
143C3×D5—31no—
144C3×D5—311no—
145C3×D5—311no—
146C3×D5—621no—
147C3×D5—9302no—
148C3×D5—4651no—
149C3×D5—4651no—
150C5×D3—51no—
151C52C3×D3×D3111yescharacteristic, complemented, Sylow
152C2×D5—4651no—
153C2×D5—4651no—
154C2×C32—1551no—
155C3×D3—51no—
156C3×D3—7751no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D3111yescharacteristic, complemented
163C3×C5D15×D3111yescharacteristic, complemented
164C3×C5D3×D15511yescharacteristic, complemented
165C3×C5C2×C3×D15511yescharacteristic, complemented
166C22×C3—23251no—
167C2×D3—7751no—
168C2×C5—151no—
169C2×C5—1551no—
170D5—31no—
171D5—311no—
172D5—9302no—
173D5—4651no—
174D5—4651no—
175C32D5×D15511yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—23251no—
178C2×C3—3101no—
179C2×C3—1551no—
180C2×C3—1551no—
181D3—51no—
182D3—7751no—
183C5—22no—
184C5C3×D15×D3111yescharacteristic, complemented
185C5C3×D3×D15511yescharacteristic, complemented
186C22—23251noSylow
187C3—21no—
188C3C3×D5×D15511yescharacteristic, complemented
189C3D15×D15511yescharacteristic, direct product factor
190C2—151no—
191C2—23251no—
192C2—1551no—
subgroupG/H
center, hypercenterC3D15×D155
commutator, cosocle, hypocenterC3×C52×C31C22×C3
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C52×C31
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×C5×D155C2semidirect
2. C3×C5×D15×C31C2semidirect
3. C3×C3⋊(C5⋊D155)C2semidirect
4. D15×D155C3direct (N × H)
6. C32×C52×C31C22semidirect
9. C3⋊(C5⋊D155)C2×C3semidirect
10. C5×D15×C31C2×C3semidirect
13. C3×C5×D155D3semidirect
14. C3×C5×D155C2×C3semidirect
20. C3×D15×C31D5semidirect
22. C32×D155D5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
32. C5×D155C3×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C2×D5semidirect
42. D15×C31C3×D5semidirect
48. C3×D155C3×D5semidirect
49. C3×D155D15direct (N × H)
55. C52×C31C2×C3×D3semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C3×D5semidirect
68. C3×C5×C31C2×C3×D5semidirect
69. C3×C5×C31C2×D15semidirect
71. C3×C5×D15D31semidirect
79. D155C3×D15direct (N × H)
84. C32×C31D52semidirect
85. C32×C52C2×D31semidirect
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×D15semidirect
99. C5×D15C3×D31semidirect
108. C3×C31C3×D52semidirect
109. C3×C31D5×D15semidirect
114. C3×D15D155direct (N × H)
118. C3×C52D3×D31semidirect
119. C3×C52C2×C3×D31semidirect
131. C32×C5D5×D31semidirect
132. C32×C5C2×D155semidirect
134. C31C3×D5×D15semidirect
142. D15C3×D155direct (N × H)
151. C52C3×D3×D31semidirect
162. C3×C5C3×D5×D31semidirect
163. C3×C5D15×D31semidirect
164. C3×C5D3×D155semidirect
165. C3×C5C2×C3×D155semidirect
175. C32D5×D155semidirect
184. C5C3×D15×D31semidirect
185. C5C3×D3×D155semidirect
188. C3C3×D5×D155semidirect
189. C3D15×D155direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×C5×D1552
C3×C5×D15×C312
C3×C3⋊(C5⋊D155)2
D15×D1553
C3×D5×D1553
C3×D3×D1555
C3×D15×D315
C3×D5×D1531